Assume that a sample is used to estimate a population proportion
p. Find the 90% confidence interval for a sample of size 247 with
146 successes. Enter your answer as an open-interval (i.e.,
parentheses) using decimals (not percents) accurate to three
decimal places.
90% C.I. =
Answer should be obtained without any preliminary rounding.
However, the critical value may be rounded to 3 decimal places.
Solution :
Given that,
Point estimate = sample proportion =
= x / n = 146 / 247 = 0.591
1 -
= 1 - 0.591 = 0.409
Z/2
= 1.645
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
= 1.645 * (((0.591
* 0.409) / 247)
= 0.051
A 90% confidence interval for population proportion p is ,
- E < p <
+ E
0.591 - 0.051 < p < 0.591 + 0.051
0.540 < p < 0.642
90% C.I. = 0.540 , 0.642
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